Finite Group Databasebeta

← #118206

Subgroups — #118206

Order 512.

535 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17809C211yesmaximal, characteristic
2#17718C211yesmaximal, characteristic
3C2×#1550C211yesmaximal, characteristic
4#17672C211yesmaximal, characteristic
5#8121C211yesmaximal, characteristic
6#7988C211yesmaximal, characteristic
7#7879C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15#1574—22no—
16#1571—21no—
17#1570—21no—
18#1565—22no—
19#1554—22no—
20#1550—22no—
21#1550—22no—
22#1548—21no—
23#1546—21no—
24#1542—21no—
25#1542—21no—
26C2×#333—21no—
27C2×#332—21no—
28#1537C414yes—
29#1531—22no—
30#1528—22no—
31#1307—22no—
32#1290—22no—
33#1277—22no—
34C22×M16—21no—
35C23×C8—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533C2×C412yes—
43#533Q812yes—
44C2×C4⋊Q8D411yescharacteristic
45C2×C4⋊Q8D411yescharacteristic
46C2×#125—21no—
47C2×C22⋊Q8—21no—
48C2×C22⋊Q8—21no—
49C2×C4×Q8—21no—
50C2×C4×Q8—21no—
51C2×#117—21no—
52C22×C42C2311yescharacteristic
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432C2×C412yes—
58#432C2×C412yes—
59#432D412yes—
60#432D412yes—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423—21no—
74#423D412yes—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8—21no—
83C2×C4⋊C8D411yescharacteristic
84C2×C4⋊C8D411yescharacteristic
85C2×C4⋊C8D412yes—
86#407—21no—
87#407—21no—
88C2×C22⋊C8—21no—
89C2×C22⋊C8—21no—
90C4×M16—21no—
91C4×M16D412yes—
92C2×#97—21no—
93C2×C4×C8—21no—
94#335—24no—
95#334—24no—
96#333—24no—
97#333—22no—
98#333—22no—
99#332—24no—
100#332—22no—
101#332—22no—
102#330—28no—
103C22×Q8—21no—
104C22×Q8—21no—
105C23×C4#4111yescharacteristic
106C23×C4#4111yescharacteristic
107C23×C4#4111yescharacteristic
108C2×M16—22no—
109C2×M16—22no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—82no—
113C22×C8—21no—
114C22×C8—21no—
115C22×C8—22no—
116C22×C8—41no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—82no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8C4⋊C412yes—
128C4⋊Q8C4⋊C412yes—
129#125—22no—
130#125—22no—
131#125—41no—
132#125—41no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8—41no—
138C22⋊Q8—41no—
139C22⋊Q8—41no—
140C22⋊Q8—41no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—41no—
146C4×Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149#117—22no—
150#117—22no—
151#117—41no—
152#117—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C22⋊C4—41no—
160C2×C42—41no—
161C2×C42C22×C411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×Q811yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42#4111yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—22no—
180C4⋊C8—21no—
181C4⋊C8—22no—
182C4⋊C8—21no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199#97—22no—
200#97—22no—
201#97—41no—
202#97C22⋊C414yes—
203C4×C8—22no—
204C4×C8—41no—
205C4×C8—41no—
206C4×C8—41no—
207C24#12611yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—81no—
213C2×Q8—81no—
214C2×Q8—82no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4#11711yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12411yescharacteristic
239C22×C4#12611yescharacteristic
240M16—44no—
241M16—82no—
242M16—82no—
243M16—82no—
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—81no—
254C2×C8—81no—
255C2×C8—82no—
256C2×C8—82no—
257C2×C8—82no—
258C2×C8—82no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—42no—
274C42—42no—
275C42C2×C22⋊C411yescharacteristic
276C42C2×C4⋊C411yescharacteristic
277C42C4×D411yescharacteristic
278C42C4×D411yescharacteristic
279C42#12011yescharacteristic
280C42#12011yescharacteristic
281C42#12011yescharacteristic
282C42#12111yescharacteristic
283C42#12111yescharacteristic
284C42#12111yescharacteristic
285C42C22⋊Q811yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42#12311yescharacteristic
289C42#12411yescharacteristic
290C42#12711yescharacteristic
291C23—22no—
292C23—22no—
293C23—41no—
294C23#38811yescharacteristic
295C23#39611yescharacteristic
296C23#39711yescharacteristic
297Q8—82no—
298Q8—82no—
299Q8—82no—
300Q8—81no—
301Q8—81no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4#38011yescharacteristic
329C2×C4#38511yescharacteristic
330C2×C4#38511yescharacteristic
331C2×C4#38611yescharacteristic
332C2×C4#38811yescharacteristic
333C2×C4#39011yescharacteristic
334C2×C4#39211yescharacteristic
335C2×C4#39311yescharacteristic
336C2×C4#39411yescharacteristic
337C2×C4#39411yescharacteristic
338C2×C4#39611yescharacteristic
339C2×C4#39911yescharacteristic
340C2×C4#47112yes—
341C2×C4#47312yes—
342C8—44no—
343C8—82no—
344C8—82no—
345C8—82no—
346C8—81no—
347C8—82no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—44no—
357C22#143911yescharacteristic
358C22#206412yes—
359C22#208012yes—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—82no—
370C4—82no—
371C4#193012yes—
372C4#201911yescharacteristic
373C4#202011yescharacteristic
374C4#204811yescharacteristic
375C4#204911yescharacteristic
376C2—22no—
377C2—22no—
378C2—41no—
379C2#1108611yescharacteristic
380C2#1112011yescharacteristic
381C2#1114511yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#178092
#177182
C2×#15502
#176722
#81212
#79882
#78792